First up, for all you DC-ists, there's a Bike Rack Design competition put on by the Golden Triangle Business Improvement District. Designs are due March 4th at 5pm, so get on it!
More info at Ready Set DC. Call for entries pdf can be seen here.
The second is not so much a competition as an opportunity to help shape the National Mall. Up until March 18 the National Park Service is seeking comments and ideas on the maintenance and future of the National Mall. Voice your opinion! Go here to fill in your ideas. Full brief and info on the National Parks Traveler site.